I'm very sorry this happened to you, you have my condolences.
Particularly if your wife is one of the travellers on the ticket, I anticipate AA will be helpful in one way or another as the death of such a close relative of a passenger is usually enough reason for allowing a change.
AA's general tariff terms at
https://www.aa.com/i18n/Tariffs/AA1.html do contain phrasing:
SALES RESTRICTIONS - 85 (CATEGORY 15)
...
- UNLESS OTHERWISE STATED IN THE INDIVIDUAL FARE RULE, EXTENSION OF TICKET VALIDITY MAY APPLY FOR DEATH/ILLNESS OF PASSENGER/COMPANION/IMMEDIATE FAMILY MEMBER.REFER TO RULE 65 (TICKETS) FOR CONDITIONS OF EXTENSION.
and
(D)EXTENSION OF TICKET VALIDITY AND WAIVER OF MINIMUM/MAXIMUM STAY PROVISIONS
- EXTENSION OF VALIDITY IF THE PASSENGER IS UNABLE TO COMMENCE OR CONTINUE HIS/HER TRAVEL DUE TO {X} DEATH OF A MEMBER OF HIS/HER IMMEDIATE FAMILY (TRAVELING OR NOT) {N}OR OF AN ASSOCIATE WITH WHOM HE/SHE IS TRAVELING OR OF THE ASSOCIATES IMMEDIATE FAMILY MEMBER, AA WILL EXTEND THE PERIOD OF VALIDITY BEYOND THE ORIGINAL LIMIT NOT TO EXCEED 30 DAYS. {N}THE DEATH MUST BE CERTIFIED IN WRITING WITH EITHER A COPY OF THE DEATH CERTIFICATE OR BY A PHYSICIAN, SPECIFYING THAT THE PASSENGER IS PREVENTED FROM COMPLETING HIS/HER JOURNEY PRIOR TO THE EXPIRATION OF THE ORIGINAL TIME LIMIT BECAUSE OF SUCH CIRCUMSTANCES. {CANCELLED}
NOTE:IMMEDIATE FAMILY MEMBER, AS USED HEREIN, MEANS SPOUSE, {N}DOMESTIC PARTNER, CHILDREN, ADOPTED CHILDREN, PARENTS, BROTHERS, SISTERS, MOTHERS-IN-LAW, FATHERS-IN-LAW, BROTHERS-IN-LAW, SISTERS-IN-LAW, DAUGHTERS-IN-LAW, SONS-IN-LAWS, GRANDCHILDREN, GRANDPARENTS. THIS INCLUDES STEPPARENTS, STEPSISTERS, STEPBROTHERS, HALF SISTERS AND HALF BROTHERS.
....
WAIVER OF SPECIAL FARE RESTRICTIONS
- (A)WHEN A PASSENGER TRAVELING AT AN EXCURSION OR SPECIAL FARE IS PREVENTED FROM TRAVELING IN ACCORDANCE WITH THE TERMS OF THE APPLICABLE TARIFF DUE TO {X} THE DEATH OF A MEMBER OF HIS/HER IMMEDIATE FAMILY OR OF AN ASSOCIATE WITH WHOM HE/SHE IS TRAVELING ON OF THE ASSOCIATES IMMEDIATE FAMILY MEMBER, THE PASSENGER WILL BE PERMITTED TO TRAVEL ACCORDING TO THE PROVISIONS BELOW.{X}
- (I)WHEN TRANSPORTATION HAS NOT COMMENCED FROM POINT OF ORIGIN
- ...
- (BB) WHEN TRAVELING AT A FARE THAT PERMITS INDIVIDUAL TRAVEL, THE PASSENGER WILL BE PERMITTED TO COMMENCE TRAVEL ON A SUBSEQUENT FLIGHT WITHOUT REGARD TO ANY PENALTY/RESTRICTIONS AFFIXED TO A SPECIAL FARE TICKET.AA WILL WAIVE, IN ACCORDANCE WITH (D)(1) ABOVE, MINIMUM OR MAXIMUM STAY PROVISIONS AFFIXED TO A SPECIAL FARE TICKET.
NOTE:TRAVEL WILL NOT BE PERMITTED ON A DAY OR AT A TIME WHEN THE FARE IS NOT APPLICABLE FOR TRAVEL NOR WILL TRAVEL BE PERMITTED TO COMMENCE AT A FARE THAT HAS EXPIRED. WHEN NECESSARY THE APPROPRIATE DIFFERENCE IN FARE WILL BE COLLECTED FROM OR REFUNDED TO THE PASSENGER.
I hope this helps you, and I would urge you to contact AA as soon as you can, even though you must have a lot of other things on your mind at the moment. If you can decide some future time to travel then do suggest that to AA now, while if you feel unable to do so then a refund or a credit in future value towards future travel might be a better thing to ask for. Do try to pick a future date or use any credit within one year of the original ticket purchase, after that I'm afraid it is harder to use.